This invention relates to a system for detecting the position and trajectory of a target and, more particularly, to a system in which the input data from the target is in the form of Doppler measurements provided by bistatic continuous-wave (CW) radar.
The first task of a target tracking system, after detecting the target and collecting Doppler measurements over a time period, is to estimate the initial values for the target time, velocity, and acceleration at a selected initialization time, e.g., at the start of the time period. Although the Doppler measurements have good velocity information on the target trajectory, track initialization is generally difficult for these systems since the Doppler measurements do not usually have good position information. Initialization is complicated further by assuming the target has maneuvering capability and that the maneuvering is not predictable.
The traditional approaches of solving the problem of trajectory initialization is to apply a nonlinear least squares (NLS) algorithm to an interval of data, or to accept a more arbitrary starting point (based in general on less data and less processing), and rely on a Kalman filter recursive algorithm to self-correct for this initialization error as new data is processed.
In order to have acceptable performance, an NLS algorithm would require a knowledge of the number of maneuvers of the target during the time period of the data. Either this number would have to be estimated from the data or the NLS could generate solutions for each of several hypothesized numbers of maneuvers and choose the hypothesis yielding the best results. In either case, the NLS could have difficulties because of the possible large number of states being estimated and the poor observability of some of these states (e.g., the start times for each maneuver).
The Kalman filter approach, which would estimate all states over the entire trajectory, would start from a generally poor initialization and rely on the filter to self-correct for this initialization error as more and more data are processed by the filter. The difficulties in this approach arise from the nonlinearity of the filter, the poor initialization, and the low quality of position information in the Doppler data. These can make filter divergence at start-up a serious problem.